Find the following integral: int frac{dx}{x^{ | vedclass

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Question

(A) We know that the standard integral formula is $\int \frac{dx}{x^{2}-a^{2}} = \frac{1}{2a} \log \left| \frac{x-a}{x+a} \right| + C$. Given integral

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$\frac{1}{8} \log \left| \frac{x-4}{x+4} \right| + C$

Vedclass · Answer

(A) We know that the standard integral formula is $\int \frac{dx}{x^{2}-a^{2}} = \frac{1}{2a} \log \left| \frac{x-a}{x+a} \right| + C$. Given integral is $I = \int \frac{dx}{x^{2}-16}$. We can write $16$ as $4^{2}$,so $I = \int \frac{dx}{x^{2}-4^{2}}$. Here,$a = 4$. Applying the formula,we get $I = \frac{1}{2(4)} \log \left| \frac{x-4}{x+4} \right| + C$. Therefore,$I = \frac{1}{8} \log \left| \frac{x-4}{x+4} \right| + C$.

Find the following integral: $\int \frac{dx}{x^{2}-16}$

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